Four wave mixing transmission line

1. A four-wave mixing radio frequency transmission line including: an input arranged to receive: a first pump signal having a first pump frequency; a second pump signal, having a second pump frequency, different from the first pump frequency; and an input signal to be amplified; a non-linear medium having an intrinsic dispersion relationship, the medium arranged to allow interaction between the input signal, the first pump signal and the second pump signal, such that the input signal is amplified and an idler signal is generated and amplified; and a plurality of dispersion control elements, the dispersion control elements arranged to alter the dispersion relationship of the medium to diverge from the intrinsic dispersion relationship at a first frequency, and at a second frequency wherein the first pump frequency is near the first frequency and the second pump frequency is near the second frequency, such that the total phase difference between the input signal, the first pump signal, the second pump signal and the idler signal is kept at zero or substantially zero as the first pump signal, the second pump signal, the input signal and the idler signal propagate down the transmission line.

2. The four-wave mixing radio frequency transmission line as claimed in claim 1 , wherein the medium and dispersion control elements are arranged such that the dispersion relationship of the medium diverges from the intrinsic dispersion relationship at the first and second frequencies, such that there are stopbands at the first and second frequencies.

3. The four-wave mixing radio frequency transmission line of claim 1 , wherein the transmission line includes bonding contacts at either end, the bonding contacts arranged to enable the transmission line to be coupled to a wider system, wherein the bonding contacts are arranged to impedance match the transmission line to the wider system, wherein the bonding contacts include: a first region having a width wider than the transmission radio frequency line, the first region for coupling the transmission line to be coupled to the wider system; and an impedance matching region gradually narrowing from the width of the first region to the width of the transmission line, wherein the impedance matching region includes curved edges as the width gradually reduces.

4. The four-wave mixing radio frequency transmission line of claim 1 , wherein the operational bandwidth of the transmission line is between a minimum operation frequency at or substantially at the first pump frequency, and a maximum operational frequency at or substantially at the second pump frequency.

5. The four wave mixing radio frequency transmission line of claim 1 , wherein idler signal is provided as an output, such that the four-wave mixing line is a frequency down-converter.

6. The four-wave mixing radio frequency transmission line of claim 5 , wherein the first pump frequency is selected based on the frequency of the input signal, to select an operational band of the frequency down converter.

7. The four-wave mixing radio frequency transmission line of claim 1 , wherein the transmission line comprises a superconducting wire; and wherein the plurality of dispersion control elements comprises a plurality of resonators.

8. The four-wave mixing radio frequency transmission line of claim 7 , wherein the transmission line comprises a plurality of Josephson junctions embedded along the transmission line.

9. The four-wave mixing radio frequency transmission line of claim 8 , wherein the transmission line is formed of a periodically repeating structure having a group of Josephson junctions connected in series, each group of Josephson junctions coupled to a dispersion control element.

10. The four-wave mixing radio frequency: transmission line of claim 7 , wherein each resonator comprises a planar capacitor and a planar inductor, such that the four-wave mixing transmission line is formed in a single plane.

11. The four-wave mixing radio frequency transmission line of claim 7 , wherein the plurality of dispersion control elements comprises one or more sets of resonators, each set of resonators comprising a plurality of resonators having the same or substantially similar resonant frequency, wherein the resonant frequency of each set of resonators defines the first frequency and the second frequency at which the dispersion relationship of the medium to diverge from the intrinsic dispersion relationship.

12. The four-wave mixing radio frequency transmission line of claim 1 , wherein the transmission line comprises a superconducting wire; and wherein the transmission line comprises a plurality of first regions where the impedance of the wire is altered, and a plurality of second regions where the impedance of the wire is altered, the first regions being of first length, and the second regions being of second length, different from the first length, the first and second regions arranged in a pattern to prevent formation of shockwaves in the transmission line, generated from third harmonics of the first and second pump signals.

13. The four-wave radio frequency mixing transmission line of claim 12 , wherein the first and second regions are arranged in a repeating pattern having two first regions followed by a second region.

14. The four-wave mixing radio frequency transmission line of claim 12 , wherein the spacing and pattern of the first and second regions determines the first frequency and the second frequency.

15. The four-wave mixing radio frequency transmission line of claim 1 , wherein the medium comprises a superconducting structure; and wherein the transmission line comprises a superconducting wire; and wherein the plurality of dispersion control elements comprises a plurality of regions where the impedance of the wire is altered, such that the wire is loaded at the plurality of regions.

16. The four-wave mixing radio frequency transmission line of claim 15 , wherein the transmission line comprises a plurality of Josephson junctions embedded along the transmission line.

17. The four-wave mixing radio frequency transmission line of claim 1 , wherein the dispersion control elements are arranged to correct phase mismatch between the pump signals, the input signal and the idler signal.

18. The four-wave radio frequency mixing transmission line of claim 1 , wherein the dispersion control elements are arranged periodically along the transmission line.

19. A four-wave mixing radio frequency method in a non-linear medium having an intrinsic dispersion relationship, the method including: providing a first pump signal having a first pump frequency in the medium; providing a second pump signal having a second pump frequency, different from the first pump signal in the medium; receiving an input signal to be amplified in the medium; enabling interaction between the first pump signal, the second pump signal and the input signal such that the input signal is amplified, and an idler signal is generated and amplified; and controlling the dispersion relationship of the medium to diverge from the intrinsic dispersion relationship at a first frequency. and at a second frequency, wherein the first pump frequency is near the first frequency and the second pump frequency is near the second frequency. such that the total phase difference between the input signal, the first pump signal, the second pump signal and the idler signal is kept at zero or substantially zero as the first pump signal, the second pump signal, the input signal, and the idler signal propagate line along the non-linear medium.